The following theorem has been proved in this paper:“the chromatic number X(G)≤3 if the graph G has no subgraph homeomorphic to K₄”,thus further getting a sufficient condition for the 3-chromatic graph. So long as the theorem similar to the above one:“the chromatic number X (G)≤4 if the graph G has no subgraph homeomorphic to K₅”can be proved，the famous“4 colour conjecture (4CC)”in the world will be confirmed.